Why would my internet in my setting show weak security?

That is one of apples new features. It should be fine, but if you want to upgrade your wifi security you can. For good security make sure your wifi uses wpa2 or higher, has a strong password, and is a hidden network.

My Apple devices show weak (WPA) security on my WiFi. I am trying to hook up a thermostat and to won't let me because of Weak security but the provider assures me that it is WPA2. A window device does not show weak security. I am told it is not a feature but a glitch

I would recommend using a safe thermostat (HomeKit enabled). One that uses apple HomeKit and home app. https://www.apple.com/ios/home/